Question

一道数学题，请详细解释一下，谢谢！

设计算法求1/1*2+1/2*3+1/3*4+…+1/49*50的值,写出用基本语句编写的程序

Answer 1

S=0 t=1
WHILE t<=50
S=1/t(t-1)
t=t+1
WEND
PRINT S
END

Answer 2

1/1*2 =( 1/1)-(1/2)

1/2*3=(1/2)-(1/3)

1/3*4=(1/3)-(1/4)

同理都是一样的

原式＝1/1-1/2+1/2-1/3+1/3-1/4……+1/48-1/49+1/49-1/50 = 1-1/50=49/50

Answer 3

double result = 0.0;
double s = 0.0;
for (int i = 1; i <= 50; i++)
{
s = i * (i + 1);
result += 1 / s;
}

Answer 4

for i:=1 to 49 do
sum:=sum+1/i*(i+1)